The Green-Schwarz formulation of the ten-dimensional superstring is one of the more intriguing approaches to string theory. Together with the Brink-Schwarz superparticle and the super-p-branes, the Green-Schwarz superstring has both a manifest spacetime supersymmetry and an obscure local worldsheet (worldline, world volume) fermionic symmetry. Preservation of this latter symmetry of the string in the presence of background
massless fields implies constraints on these background fields which are equivalent to their classical equations of motion. This correspondence underlies a twistor-like transform in ten dimensions. When formulated in a curved background superspace, the superstring defines an equivalence relation on superspace geometries which explains the equivalence of differing formulations of supergravity in superspace. These developments in
classical superobjects are reviewed in this report, and we make some comments on recent progress in their quantization.